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Automated study of a regular trifolium. (English) Zbl 1488.51014

Summary: We present a study of a classical plane real curve in a technology-rich environment. The interplay between implicit and parametric presentations is enhanced. Cooperation of a computer algebra system and of a dynamical geometry system enables to discover properties that may be hidden in hand-made computations. Moreover, technology does not act only as a solver, but the outputs reveal a need to expand the framework from geometry over the reals to some usage of complex variables. The paper is a case study of an undergraduate approach, that is, its main audience is educators at the university level.

MSC:

51M35 Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations)
68W30 Symbolic computation and algebraic computation

Software:

CoCoA; GeoGebra
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Full Text: DOI

References:

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